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Wednesday, October 19, 2005

Uh-Oh This is going to be Difficult!!!!

Well folks once again I'm scribe and I think it'll be the hardest class to cover so far this year. These are the reasons:
-for those of you who were here today you know how complicated this class was
-for those of you who weren't here today I'm going to have to explain this in a very detailed manner
-and I do not have a Windows computer (I have an iMac) and my only drawing program isn't responding so I'm on my own with the examples.


Here we Go!

Today's class was with Mr. Clark and he taught us "Rational Equations". Right off the hop he went into just a little review of what we needed to remember from previous years of Rational Expressions.

The first thing that you must recall is that with Rational Equations there is an answer and a RESTRICTION. As long as there is a denominator with a variable there will be a value that "x" cannot equal. (Restriction or Non-Permissable Value).
To get this value you must make all the denominators with a variable in them equal to zero. Do this by solving the equation:

_7_ or ____3a____ = ____3a____
x-3 --> x-3 cannot equal 0 a^2-2a-15 (a+3)(a-5) --> a+3 c.e. 0 & a-5 c.e. 0
x cannot equal 3 a c.e. -3 a c.e. 5
a c.e. -3,5

Next thing you must recall about Rational Equations is that when adding and subtracting expressions with a denominator you must put all terms over a LCD (Lowest Common Denominator). Do this by finding the factors of the denominator. Once you have factored all of the denominators find the number(s) that are common and multiply them together and then find the numbers left over and multiply them into the product (if there is only one term with a denominator, use it for all expressions in the equation):

_x_ + _2x_ - _1_
10 12 50 --> {2,5,5} 2 is common to all three --------> 2 2,3,and 5 are left over:
----------> {2,3,2} 5 is common to two of the terms--> *_5_
------------------> {2,5} 10 2*3*5*10= 300
LCD = 300

5x^2 y 10x^3 y^3 15x^2 y^5 --> {3,5,x,x,y,y,y,y,y} 5,x,x,y are common to all three 5*x*x*y*y*y*1*2*3*x*y*y
------------------> {2,5,x,x,x,y,y,y} y,y are common to two =5*1*2*3*x*x*x*y*y*y*y*y
-----------------------------> {1,5,x,x,y} 1,2,3,x,y,y are left over =30 x^3 y^5




After this we were given four examples on the board, all of different difficulty. Yes, I will try to show how to solve them:

A) _x-2_ + _3x_ - _3x-8_ = 1 B) _2m-9_ + _m_ = _5_
6 8 24 m-7 2 m-7

C) __5__ - ____2y-4____ = _3_ D) ____4____ - ____5____ = ____3____
2y+6 y^2-y-12 y-4 x^2+2x-15 x^2-x-6 x^2+7x+10


First find the LCD of the equation which is. Now multiply each term in the equation by the LCD. Cancel out from the LCD with the denominator as needed then multiply the numerator by whatever is left. Then find and combine the like terms. Now solve for x:
*NOTE: factoring or quadratic formula may be needed to solve for x.


A) _x-2_ + _3x_ - _3x-8_ = 1 B) _2m-9_ + _m_ = _5_
6 8 24 m-7 2 m-7

24{_x-2_} +24{_3x_} -24{_3x-8_} = 24{1} 2(m-7) {_2m-9_} +2(m-7) {_m_} = 2(m-7) {_5_}
{ 6 } { 8 } { 24 } { m-7 } { 2 } {m-7}

4{x-2} + 3{3x} - 1{3x-8} = 24{1} 2 {2m-9} + (m-7) {m} = 2 {5}

4x-8 + 9x + -3x+8 = 24 4m-18 + m^2-7m = 10

10x = 24 m^2-3m-28 = 0

x = 12/5 (m-7) (m+4) = 0

m-7=0 m+4=0

m=7 m=-4

m=7,-4 ; m c.e. 7 .: m=4


C) __5__ - ____2y-4____ = _3_
2y+6 y^2-y-12 y-4

__5__ - ____2y-4____ = _3_
2(y+3) (y-4) (y+3) y-4

[2(y+3)(y-4)] {__5__} -[2(y+3)(y-4)] {____2y-4____} = [2(y+3)(y-4)] {_3_}
2(y+3) (y-4) (y+3) y-4

(y-4) {5} - 2 {2y-4} = 2(y+3) {3}

5y-20 + -4y+8 = 6y+18

-5y = 30

y = -6 ; y c.e. -3,4 .: y=-6


D) ____4____ - ____5____ = ____3____
x^2+2x-15 x^2-x-6 x^2+7x+10

_____4____ - ____5____ = ____3____
(x+5) (x-3) (x-3) (x+2) (x+5) (x+2)

[(x+5) (x-3) (x+2)] {____4____} -[(x+5) (x-3) (x+2)] {____5____} = [(x+5) (x-3) (x+2)] {____3____}
{(x+5) (x-3)} {(x-3) (x+2)} {(x+5) (x+2)}

(x+2) {4} - (x+5) {5} = (x-3) {3}

4x+8 + -5x-25 = 3x-9

-4x = 8

x = -2 ; x c.e. 3,-5,-2 .: x= NO SOL'N


Phew! Done.

Well that was today's class. BTW Mr. Clark assigned exercise # 19, a "Rational Equations" worksheet, and an "Algebra Review" sheet.

Once again sorry that my computer wasnt cooperating, I tried my best.


Oh Yeah! tomorrow' scribe is umm...

... Kasia (sorry I picked you again). Don't worry yours won't be as difficult as mine was.

1 Comments:

At 10/19/2005 9:18 PM, Blogger AichelleS. said...

good job Craig

 

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